Just a thought. If you have a bad connection or crimp at the battery, either ground or hot side, you could get a low voltage drop out situation.
Explanation: The master solenoid is hot all the time and switched to ground through the master switch. When the solenoid is closed, only a few amps of current ever flow through it, rarely more than 10 to 15 amps. At that level of current a one volt voltage drop at a bad battery cable crimp wouldn't be noticeable. If resistance = volts / amps, then the resistance is 1 volt divided by, say, 15 amps or .066 ohms. BUT, when you are cranking the starter motor the current flow will go up to 100 amps or more. During start up, that means that the voltage drop at that bad crimp will be, volts = amps x ohms, or 100 x .066 = 6.6 volts. That's the voltage drop JUST at the bad crimp. That means that your 12 volts from the battery, minus 6.6 volts at the bad crimp leaves you with 5.4 volts at the starter. If this happens, the solenoid will lose the voltage/amps at it's coil (remember that its wired hot to battery) and release. The moment the contacts break connection, the voltage is back to 12 volts and the solenoid immediately tries to close. This is what can cause the chatter. And if it only happens when your cranking the starter, you won't hear it or notice it.
If you think this is to extreme to be plausible, do the math with a half volt drop at a bad crimp. This means that you would still have a 3.3 volt drop just at the bad connection, leaving 8.7 volts at the starter. Still well below the 'danger zone' for drop out.
With all the trouble you've had, I'd recommend new ground cable, and new battery positive cables from the battery to the master solenoid terminal (inside and outside of the battery box).
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